Geometric realizations of Ringel-Hall algebras of continuous quivers of type A

2025/11/27 by Zhao, Minghui
#16G20 #17B37 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2511.22051

Abstract

Lusztig introduced the geometric realizations of quantum groups associated to finite quivers and defined their canonical bases. Sala and Schiffmann introduced the Ringel-Hall algebra of line and realized it as the direct limit of Ringel-Hall algebras of finite quivers of type A. In this paper, we shall give geometric realizations of Ringel-Hall algebras of continuous quivers of type A via the geometric realizations of Lusztig by using the method of approximation given by Sala and Schiffmann.

Citations

• Continuous Nakayama Representations
• Decomposition of Pointwise Finite-Dimensional S¹ Persistence Modules
• Continuous Quivers of Type A (IV) Continuous Mutation and Geometric Models of \mathbf E-clusters
• Continuous Quivers of Type A (III) Embeddings of Cluster Theories
• Continuous Quivers of Type A (II) The Auslander-Reiten Space
• Continuous quivers of type A (I) Foundations
• Decomposition of persistence modules
• Ringel-Hall algebras beyond their quantum groups I: Restriction functor and Green's formula
• Interval Decomposition of Infinite Zigzag Persistence Modules
• Decomposition of pointwise finite-dimensional persistence modules
• Lectures on canonical and crystal bases of Hall algebras

Related

• Structure coefficients for quantum groups
• Geometric approach to Hall algebra of representations of Quivers over local ring
• Quantum Borcherds-Bozec algebras via semi-derived Ringel-Hall algebras
• The Parity of Lusztig's Restriction Functor and Green's Formula
• Ringel-Hall algebra construction of quantum Borcherds-Bozec algebras